非负DAG学习：基于伴随估计
Nonnegative DAG Learning via Concomitant Estimation
- Northeastern University（东北大学）
- University of Rochester（罗切斯特大学）
- King Juan Carlos University（胡安·卡洛斯国王大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出NoCo估计器，通过伴随估计与对数行列式约束，在非负权重下直接施加无环性，联合学习DAG结构及噪声方差，提升恢复性能。
AI中文摘要：
我们研究从观测数据中学习具有非负边权的有向无环图（DAG）的问题。我们提出了非负与伴随（NoCo）DAG估计器，该估计器在线性结构方程模型中联合恢复加权图结构和观测数据的外生噪声方差。与现有技术不同，这种噪声自适应公式将平滑的伴随lasso准则与更简单的对数行列式无环性约束相结合，该约束利用非负性并产生更良性的优化景观。具体而言，非负权重允许我们直接在邻接矩阵上施加无环性，而无需对其元素进行逐元素平方，从而避免了众所周知的Karush-Kuhn-Tucker条件的退化问题。在计算上，我们开发了一种乘子法算法，该算法适用于同方差和异方差噪声分布。在每次迭代中，我们使用块连续凸近似来最小化增广拉格朗日函数，在邻接矩阵的近端梯度步骤和噪声尺度的闭式更新之间交替进行。模拟实验表明，在各种设置下，NoCo相对于竞争方法在结构和边权恢复方面均有改进，凸显了利用非负性和噪声自适应性的优势。
英文摘要：
We study the problem of learning directed acyclic graphs (DAGs) with nonnegative edge weights from observational data. We propose the Nonnegative and Concomitant (NoCo) DAG estimator, which jointly recovers the weighted graph structure and the exogenous noise variances in the linear structural equation model for the observations. Different from prior art, this noise-adaptive formulation blends a smoothed concomitant lasso criterion with a simpler log-determinant acyclicity constraint that exploits nonnegativity and yields a more benign optimization landscape. Specifically, nonnegative weights allow us to impose acyclicity directly on the adjacency matrix without elementwise squaring of its entries, thus avoiding the well-documented degeneracy of the Karush-Kuhn-Tucker conditions. Computationally, we develop a method of multipliers' algorithm that accommodates both homoscedastic and heteroscedastic noise profiles. Within each iteration, we use block successive convex approximation to minimize the augmented Lagrangian, alternating between proximal gradient steps for the adjacency matrix and closed-form updates for the noise scales. Simulated experiments demonstrate NoCo's improved structural and edge-weight recovery relative to competing methods in a variety of settings, highlighting the benefits of exploiting nonnegativity along with noise adaptivity.
